Question

Alice drew a rectangle with a perimeter of 30 cm and an area of 56 cm2. Which dimensions match Alice's rectangle?

Answer 1

Answer:

The dimensions that match Alice's rectangle are 7 cm and 8 cm.

Step-by-step explanation:

The perimeter of the rectangle is given by:

$P = 2(a + b) = 30 cm$    (1)                              

Where a and b are the sides of the rectangle

Also, the area of the rectangle is:

$A = a\times b = 56 cm^{2}$   (2)

By solving equation (1) for a, we have:

$a = 15 cm - b$      (3)                      

Now, by entering equation (3) into (2) we can find one side of the rectangle:

$56 cm^{2} = (15 cm - b)\times b$          

$b^{2} - 15b + 56 = 0$                                                        

Solving the above quadratic equation we have:

b₁ = 7 cm  and b₂ = 8 cm                      

Now, the other side of the rectangle can be calculated with equation (3):

$a = 15 cm - b_{1} = 15 - 7 cm = 8 cm$                          

or    

$a = 15 cm - b_{2} = 15 - 8 cm = 7 cm$            

Taking the first solution (b₁) or the second (b₂), we find that the dimensions that match Alice's rectangle are 7 cm and 8 cm.          

Therefore, the dimensions that match Alice's rectangle are 7 cm and 8 cm.

                                               

I hope it helps you!